Grain growth from homogeneous initial conditions: Anomalous grain growth and special scaling states.

We used the large-g Potts model on a two-dimensional lattice to study the evolution of the disordered cluster developed from a perfect hexagonal lattice with a single defect. The distribution functions were not stable, while the average area and the number of grains in the cluster grew linearly in time. However, the grains at the boundary of the cluster formed a well defined region which reached a special scaling state with time invariant distributions but no scale change, contrary to the result of Levitan [Boris Levitan, Phys. Rev. Lett. 72, 4057 (1994)].The rate of propagation of disorder is the same as the rate of growth of the cluster. Abnormal grain growth can occur without anisotropy of surface energy. It requires only widely spaced, modest size differences in an initially homogeneous array of grains.